Research
My research interests lie in number theory and arithmetic geometry. In particular, I am interested in (torsion of) elliptic curves and lowdimensional abelian varieties, often in the case of extra endomorphisms and from the vantage of rational points on modular and Shimura curves, and lowdegree points on curves and higherdimensional varieties.
Preprints

Bielliptic Shimura curves \(X_0^D(N)\) with nontrivial level (computations), (preprint)
with Oana Padurariu 
CM points on Shimura curves via QMequivariant isogeny volcanoes (computations), (preprint)

CM elliptic curves: volcanoes, reality and applications, part II (preprint)
with Pete L. Clark
Publications
 The least degree of a CM point on a modular curve (computations), (pdf)
with Pete L. Clark, Tyler Genao, and Paul Pollack
Journal of the London Mathematical Society, 2022

ChevalleyWarning at the boundary (pdf)
with Pete L. Clark and Tyler Genao
Expositiones Mathematicae, 2021 
Classically integral quadratic forms excepting at most two values (arXiv)
with Madeleine Barowsky, Will Damron, Andres Mejia, Nolan Schock, and Kate Thompson
Proceedings of the AMS, 2018
Conferences and Workshops
Contributed Talks

A volcanic approach to CM points on Shimura curves (slides)
SRNTC, Louisiana State University – March 2023  A volcanic approach to CM points on Shimura curves (slides)
JMM Special Session on Arithmetic Geometry Informed by Computation, Boston, MA – January 2023 
A volcanic approach to CM points on Shimura curves (slides)
PANTS XXXV, University of South Carolina – December 2022 
A volcanic approach to CM points on Shimura curves
Graduate Summer Conference, UGA – July 2022 
Fields of moduli, rationality, and fake elliptic curves
Graduate Summer Conference, UGA – July 2021 
No elliptic curve has a Qrational point of order 13
Graduate Summer Conference, UGA – July 2020 
Triangular numbers and modular forms
Graduate Summer Conference, UGA – July 2019 
An axiomatic approach to homology theory
Graduate Summer Conference, UGA – July 2018  Classically integral quadratic forms excepting at most two values (slides)
with M. Barowsky, W. Damron, A. Mejia, and N. Schock
Joint Math Meetings, Atlanta, GA – January 2017
Attendee

Virtual Number Theory and Arithmetic Geometry (VaNTAGe)
Virtual – Fall 2020, Summer 2021, Fall 2021 
PCMI Graduate Summer School on
Number Theory Informed by Computation
Virtual – July 2021 
Mathematics TeacherScholar Symposium (MaTSS)
Virtual – May 2021 
Connecticut Number Theory Conference (CTNT)
Virtual – June 2020 
Front Range Number Theory Day
Virtual – April 2020 
Arithmetic Geometry is Online In Zoom, Everyone (AGONIZE)
Virtual – March 2020 
Arizona Winter School  Nonabelian Chabauty
University of Arizona – March 2020 
Modular Forms, Arithmetic, and Women in Mathematics (MAAIM)
Emory University – Nov 2019 
Midwest Arithmetic Geometry and Number Theory Series (MAGNTS)
Ohio State University – Oct 2019 
CMIHIMR Summer School in Computational Number Theory
University of Bristol – June 2019 
Connecticut Summer School in Number Theory and
Conference on Elliptic Curves and Modular Forms (CTNT)
University of Connecticut – May 2018
Seminar Talks

A volcanic approach to CM points on Shimura curves (slides)
Algebra & Number Theory Seminar, Emory University – March 2023 
On Hindry–Silverman’s Sur le nombre de points de torsion rationnels sur une courbe elliptique Short and Sweet Seminar (SASS), UGA – October 2022

A volcanic approach to CM points on Shimura curves (slides)
Number Theory Seminar, UGA – September 2022 
The Chebotarev density theorem
Catalan’s Conjecture after Mihailescu (CCAM) Reading Seminar, UGA – November 2021 
Isogeny volcanoes
Graduate Student Seminar, UGA – October 2021  On Honda’s Isogeny classes of abelian varieties over finite fields
Classical Readings in Arithmetic/Algebraic Geometry Seminar (CRAAG), UGA – July 2021 
What is a Shimura curve?
Graduate Student Seminar, UGA – April 2021  Locally algebraic representations
Serre on Zoom (SeZoom) reading seminar, UGA – March 2021

Galois action on CM points
Zannier on Zoom (ZaZoom) reading seminar, UGA – October 2020 
Sporadic CM points on Modular Curves
Graduate Student Seminar, UGA – April 2020 
Formalism of moduli problems
Arithmetic Moduli of Elliptic Curves Reading Seminar, UGA – Nov 2019 
Introduction to Sage and Magma
Street Math and Related Topics Seminar (SMARTS), UGA – Nov 2019 
Modular forms part 2
Arithmetic Moduli of Elliptic Curves Reading Seminar, UGA – Aug 2019 
Introduction to modular forms
Graduate Algebraic Geometry Seminar, UGA – March 2019